Spectral Compressive Imaging (SCI) reconstruction is inherently ill-posed, offering multiple plausible solutions from a single observation. Traditional deterministic methods typically struggle to effectively recover high-frequency details. Although diffusion models offer promising solutions to this challenge, their application is constrained by the limited training data and high computational demands associated with multispectral images (MSIs), complicating direct training. To address these issues, we propose a novel Predict-and-unmixing-driven-Subspace-Refine framework (PSR-SCI). This framework begins with a cost-effective predictor that produces an initial, rough estimate of the MSI. Subsequently, we introduce a unmixing-driven reversible spectral embedding module that decomposes the MSI into subspace images and spectral coefficients. This decomposition facilitates the adaptation of pre-trained RGB diffusion models and focuses refinement processes on high-frequency details, thereby enabling efficient diffusion generation with minimal MSI data. Additionally, we design a high-dimensional guidance mechanism with imaging consistency to enhance the model's efficacy. The refined subspace image is then reconstructed back into an MSI using the reversible embedding, yielding the final MSI with full spectral resolution. Experimental results on the standard KAIST and zero-shot datasets NTIRE, ICVL, and Harvard show that PSR-SCI enhances visual quality and delivers PSNR and SSIM metrics comparable to existing diffusion, transformer, and deep unfolding techniques. This framework provides a robust alternative to traditional deterministic SCI reconstruction methods. Code and models are available at https://github.com/SMARK2022/PSR-SCI.